A number of times I have encountered in text-books and articles that neutrinos might contribute only a small fraction to dark matter. The reason has to do with the fact that if all of the dark matter consisted of neutrinos, then small-scale structures in the Universe could not have formed yet, because, as they say, neutrinos "wash out" small fluctuations. However, none of these texts provided a reference to any specific sources explaining in detail what is meant by "washing out". After all, neutrinos are notorious in their weak interaction with baryonic matter, so if there is a small-scale fluctuation of baryons, then how background neutrinos can prevent it from growing further if they practically do not interact with baryons? I guess the question boils down to calculating cross-sections of interactions at specific temperatures. I would appreciate comments and references to sources addressing this particular issue.
2 Answers
We know matter started out evenly spread, because the cosmic microwave background is extraordinarily homogeneous. And yet we know the first galaxies were forming barely half a billion years after the Big Bang. So the aggregation of matter to form large gravitational structures was extraordinarily quick.
It's relatively straightforward to model how fast the perturbations seen in the CMB would have grown, putting in various conditions like the density of matter, and generally speaking if we start with cold dark matter the growth rate is fast enough. NB visible matter wouldn't have been able to create galaxies so fast on its own because its density simply isn't great enough. The galaxies formed so fast because the much higher density dark matter was able to form gravitationally bound structures and the baryonic matter followed it into the wells.
However in the big bang neutrinos were created with relativistic velocities, and it's exceedingly difficult to form gravitationally bound structures from fast moving objects. The velocity of the objects will always be far above the local escape velocities. If all dark matter were neutrinos it would take an enormous time to form gravitationally bound structures because it's exceedingly hard for neutrinos to lose their energy and slow down enough.
And this is why the dark matter can't be neutrinos. It isn't that the neutrinos in some way stop baryonic matter from forming gravitationally bound structures, but rather that baryonic matter required help from dark matter to form those structures fast enough. Neutrinos could not have provided that help.
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The dark matter energy density of the universe is, at present, thought to be about five times that of the baryonic matter energy density. Meanwhile, the radiation energy density is almost negligible. Matter energy is about 4.5% of the total energy density of the universe. Dark matter makes up about 23%, and radiation is very small at about 0.009%. The number for radiation was calculated including all relativistic particles, including neutrinos. In fact, if you go through and read this link, it details the calculation for the total neutrino energy density and shows that it is thought to be about 68% of the photon energy density. So the 0.009% of the universe that is relativistic particles is not even mostly neutrinos.
My point? There truly is simply not enough neutrinos out there to explain away dark matter as neutrinos. Not only that, but we have clearly already included them in the calculation. Dark matter makes up 22.7% (give or take) of the energy density of the universe. And that is on top of the less than 0.0036% that neutrinos account for. So there's no way that neutrinos could be a major, let alone sole, component of dark matter.
For an overview of the energy densities, see Wikipedia and links therein
To answer your question on "washing out", the Wikipedia article on Dark Matter does a very good job at explaining this. For small scale structure to form, dark matter is required to help gravitationally bind baryonic matter. However, the free streaming length of any candidate particle that accomplishes this must be small. The free streaming length is the distance that the particles move in the early universe from random motions before the expansion slows them down. Primordial density fluctuations provide the seeds for small scale structure to form, but if the free streaming length of the dark matter candidate particle is larger than the scale of the small primordial perturbations, then these perturbations become homogenized (or "washed out") as the particles communicate and equilibrate. Without the perturbations, there is no seed for the small scale structure and, thus, it does not form.
Now you may be wondering why dark matter is needed in the first place for small scale structure to form. After the Big Bang, ordinary baryonic matter had too much temperature and pressure to collapse into structure on its own. It requires a gravitational seed (like giving it a kick-start to get the gravitational collapse going), which means there has to be a perturbation in the density of a colder, less interacting form of matter to provide this seed; that is, a local density of this cold dark matter that is higher than the background value. These perturbations would be formed because of the primordial density perturbations left over from inflation. However, neutrinos are known to have a high free streaming length, thus they would smooth out these perturbations in their own density and you wouldn't get a local high density region that could act as a seed. No seed means no collapse. No collapse means no small scale structure (until it's much too late). Neutrinos are actually the primary candidate for hot dark matter, but they are not a viable consideration for cold dark matter, which is what is necessary to generate sufficient small scale structure formation.
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